Solve for $x$ : $x^2 - 4x - 32 = 0$
Answer: The coefficient on the $x$ term is $-4$ and the constant term is $-32$ , so we need to find two numbers that add up to $-4$ and multiply to $-32$ The two numbers $-8$ and $4$ satisfy both conditions: $ {-8} + {4} = {-4} $ $ {-8} \times {4} = {-32} $ $(x {-8}) (x + {4}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -8) (x + 4) = 0$ $x - 8 = 0$ or $x + 4 = 0$ Thus, $x = 8$ and $x = -4$ are the solutions.